muscle-ups: improved approximations of the matter field with the extended Press–Schechter formalism and Lagrangian perturbation theory

Abstract

Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are invaluable tools to generate large suites of mock halo catalogues. In this paper, we first show that the main limitation of current semi-analytical schemes to simulate the displacement of CDM is their inability to model the evolution of overdensities in the initial density field, a limit that can be circumvented by detecting halo particles in the initial conditions. We thus propose ‘MUltiscale Spherical Collapse Lagrangian Evolution Using Press-Schechter’ (muscle-ups), a new scheme that reproduces the results from Lagrangian perturbation theory on large scales, while improving the modelling of overdensities on small scales. In muscle-ups, we adapt the extended Press and Schechter (EPS) formalism to Lagrangian algorithms of the displacement field. For regions exceeding a collapse threshold in the density smoothed at a radius R, we consider all particles within a radius R collapsed. Exploiting a multi-scale smoothing of the initial density, we build a halo catalogue on the fly by optimizing the selection of halo candidates. This allows us to generate a density field with a halo mass function that matches one measured in N-body simulations. We further explicitly gather particles in each halo together in a profile, providing a numerical, Lagrangian-based implementation of the halo model. Compared to previous semi-analytical Lagrangian methods, we find that muscle-ups improves the recovery of the statistics of the density field at the level of the probability density function (PDF), the power spectrum, and the cross correlation with the N-body result.

Large-scale dark matter simulations

“…In an alternative approach, Kitaura and Hess (2013) replaced the LPT displacement field on smallscales by values motivated from spherical collapse (Bernardeau 1994;Mohayaee et al 2006). A similar idea is implemented in MUSCLE (Neyrinck 2016;Tosone et al 2021). Numerous models have been developed based on an extension of the predictions of LPT via various small-scale models that aim to capture the collapse into halos or implement empirical corrections: PATCHY (Kitaura et al 2014), PTHALOS (Scoccimarro and Sheth 2002;Manera et al 2013), EZHALOS (Chuang et al 2015a), HALOGEN (Avila et al 2015).…”

Large-scale dark matter simulations

“…in Muscle (Neyrinck 2016;Tosone et al 2021). Numerous models have been developed based on an extension of the predictions of LPT via various small-scale models that aim to capture the collapse into halos or implement empirical corrections: Patchy (Kitaura et al 2014), PTHalos (Scoccimarro and Sheth 2002;Manera et al 2013), EZHalos (Chuang et al 2015a), HaloGen (Avila et al 2015).…”

Mapping Lyman-alpha forest three-dimensional large scale structure in real and redshift space

“…To this end we take the dark matter field from the reference simulation down-sampled to the chosen resolution. A large number of fast gravity solvers are now available achieving that accuracy at those high redshifts (z = 2) on Mpc scales (Kitaura & Hess 2013;Tassev et al 2013;Feng et al 2016;Tosone et al 2021). Then we make a suitable non-linear transformation of that field which improves the bias mapping relation to the targeted tracer distribution.…”

“…The accuracy of the Lyα forest modelling methods is expected to be increased when using (fast) N -body codes rather than approximated gravity solvers, which fail to model the evolution of cosmic structures beyond the mildly non-linear regime. However, given the high redshift of the data and when the studies are restricted to large scales of say, above ∼ 5 h −1 Mpc, fast methods correcting for shell-crossing may be accurate enough (Kitaura & Hess 2013;Tosone et al 2021).…”